Temperature and heat

1
Temperature and heat

• Phys 2101
• Gabriela González

2
Temperature

• Zeroth law of thermodynamics
• If bodies A and B are each in thermal equilibrium
  with a third body T, then they are in thermal
  equilibrium with each other.
• Or every body in thermal equilibrium has a well
  defined temperature. When two bodies have the
  same temperature, they are in thermal
  equilibrium.

3
Temperature Scales
Lord Kelvin (1824-1907)
Anders Celsius1701-1744

• On small scale, temperature is a measure of the
  vibration of the atoms in the material (solid,
  gas or fluid).
• SI unit kelvin (K)
• There is an absolute minimum temperature (when
  all the atoms are still). That temperature is
  zero kelvin.
• There is a special temperature at which ice,
  water and vapor coexist triple point of water.
  This temperature is defined as 273.16 K (the
  triple point happens at a pressure of 611 Pa).
• Other common scales
• Celsius (oC) TcT-273.15. Freezing water
  temperature at 1at 0oC, boiling water
  temperature is 100oC.
• Fahrenheit (oF) TF(9/5)TC32.
• Normal Body temperature is 98.6 oF. What is it
  in kelvins and oC?
• Comfort level is usually accepted to be 68oF.
  What is it in kelvins and oC?

Fahrenheit, Daniel Gabriel (1686-1736)
4
Thermal Expansion

• When temperature changes, solid bodies change
  their length, and all bodies change their volume
  according to
• ?L L ? ?T
• with ? coefficient of linear expansion
• ?V V ? ?T
• with ? coefficient of volume expansion
• If a body has a length L0 at temperature T0,
  what is its length at a temperature T?

L L0?L L0L0 ? ?T L0 (1? ?T)
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Expansion gaps (joints)

• A highway is made of concrete slabs that are 15m
  long at 20oC.
• If the temperature range at the location of the
  highway is from -20oC to 40oC, what size
  expansion gap should be left (measured at 20oC)
  to prevent buckling of the highway? Concrete has
  a coefficient of linear expansion ?12 x 10-6
  K-1
• How large are the gaps at -20oC?
• What is the temperature range in degrees
  Fahrenheit?

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Thermal Coefficients

• For most elements, density decreases linearly
  with temperature. If ? is the coefficient of
  thermal volume expansion, what is the coefficient
  of thermal density decrease?
• For solid bodies, it is usually true that ?3?.
  Is this a coincidence?
• Can ? be a function of temperature? What does it
  mean if ? is negative?

Water density vs. temperature
Why does ice float on water?
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Temperature, Heat and heat capacity

• Temperature is a property of systems in thermal
  equilibrium.
• Heat is energy transferred between systems at
  different temperatures.
• When talking about heat, we usually use the
  symbol Q. The SI unit for heat is the Joule.
  However, more common units are Btu (British
  thermal unit) and calories
• 1 Btu 1055 J
• 1 cal 4.186 J (1 Cal 1kcal 1,000 cal)
• The heat capacity C of an object is the
  proportionality constant between heat absorbed
  and resulting change in temperature
• Q C ?T C (Tf-Ti)
• SI units for C are J/k, but common units are
  cal/oC.

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Heat capacity, heat of transformation

• Heat capacity, like volume or mass, is a
  property that depends on the amount of material
  we are considering. A property that only depends
  on the substance (like density) is specific heat
  cC/m ? Q c m ?T
• The specific heat of water is
• c 1 cal/(goC) 1 Btu/(lboF)
  4190 J/kg K
• When a material undergoes a phase transformation
  (it is melting, or boiling), the temperature will
  not change, but heat is absorbed (or emitted) in
  the transformation. The energy per unit of mass
  is called the heat of transformation L
• Q
  L m

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Example

• What is the amount of energy required to melt
  100g of silver at room temperature?
• First, we need to get the silver to the
• melting temperature, 1235K from room
  temperature, 293K
• Q1 cAgm?T 236 (J/kgK) x 0.1 kg x
  (1235K-293K)22,231 J
• Then, we need to melt the silver
• Q2 Lm 105 kJ/kg x 0.1kg 10,500 J
• Total energy required
• Q Q1Q2 32,731 J 31 Btu 7.8 Cal

A--Granulating ladles. B--Wind furnace.
C--Another wind furnace made of potter's clay, on
a tripod. D--Crucible in which the silver is
melted. E--Crucible used as ladle. F--Copper
basin for drying the granules. G--An iron grate
on which to heat the silver. H--The man who
granulates. K--The man holding the broom.
Treatise on the foremost mineralogy and
metallurgy (1598)
http//oldsite.library.upenn.edu/etext/collections
/smith/ercker/